# Hedonic pricing for laptops

I read an interesting article about hedonic pricing and I thought I’d try this out for some product. Hedonic pricing refers to breaking down a product into features and evaluating how much each of those features contribute to a product’s overall price. As a result, you’ll be able to see which features are valued most by consumers. This can help with pricing new products, but possibly it can also reveal in which area R&D activity should be concentrated.

In this post I’ll present the results of a simple hedonic pricing exercise I did for laptops. I evaluated the 101 most popular laptops (the first roughly 20 from each of the laptop price categories) on Amazon according to screen size, CPU, memory, hard drive size, GPU and two other features (1. does it have a touchscreen?, 2. is it a Mac?).

A few words on measurements: screen size was measured in inches, CPU in Ghz, memory and hard drive size in gigabytes. The GPU was an indicator variable taking on three possible values: 1 for an entry-level card, 2 for a mid-range card and 3 for a high-range card. Touchscreen and Mac were just dummy variables, e.g. 0 if there is no touchscreen / laptop is not a Mac, 1 otherwise. Ultrabooks, chromebooks and any other “fancy” thing that is not a laptop per se were excluded.

One idea behind hedonic pricing is to use a log-lin regression, which takes the form

$\ln Y_i = \alpha + \beta_1 X_{1i} + ... + \beta_k X_{ki} + \epsilon_i.$

Given that the betas are the slope coefficients of ln Y with respect to their respective X’s, we have that

$\beta_j = \frac{\partial \ln Y}{\partial X_j} = \frac{1}{Y} \frac{\partial Y}{\partial X_j} = \frac{\partial Y/Y}{\partial X_j}.$

If we let dX be 1, then this simplifies to dY/Y, which is just the percentage change in the dependent variable. In other words, the betas will tell us by how what percentage the dependent variable (Y) would change, if the respective independent variable (X) were to increase by one unit, holding everything else constant.

The model I estimated for laptops is

$\ln PRICE = 6.2127 - 0.0154 SCR + 0.0578 CPU + 0.1158 RAM - 0.0002 HDD + 0.3235 GPU + 0.2657 TS + 0.4988 MAC + \epsilon.$

The intercept, memory (RAM), GPU and the Mac dummy are significant at the 1% level. Hard drive size (HDD) and the touchscreen dummy (TS) are significant at 10%. The rest are not significant.

Meaning that screen size (SCR) and CPU (at least when measured purely by Ghz) are not good predictors of a laptop’s price. In other words, a larger screen or a better CPU is not valued higher on average. This could be because of some users’ preference towards smaller screens, and possibly because a better CPU has diminishing returns in terms of performance (relative to more memory for instance).

Based on the regression results (p=0.09501, wrong sign) and my personal judgment, I would also say that the size of the hard drive doesn’t have a significant effect on price either. Many people prefer larger hard drivers but they’re not willing to pay too much for them. And many people prefer smaller but faster hard drives (SSD for instance), and are willing to pay a premium for those. Therefore, hard drive size has an ambiguous effect on price.

Having a touchscreen does increase the price, but since the sample had only 8 laptops with touchscreens, their precise effect cannot be pinpointed. It can be anywhere between 0% and 50% price premium. The regression coefficient says 26.6%, but then again treat this with caution.

The price premium of Macbooks is also hard to specify. The sample only had 10 Macs and the price premium lies somewhere between 18% and 81%. With the average being around 50%. In any case, we can clearly see that Macbooks enjoy a comfortable price advantage in the market.

If one wanted a mid-range GPU instead of an entry level one, he’d have to pay a price premium of around 32%, twice that if he wanted a high-end GPU. The confidence interval, however, is between 11% and 54%. But here as well, we can see that GPU’s do influence the price significantly.

Finally, the most precise predictor of price is memory. To have 1 GB additional RAM, you’d have to pay 12% more. The confidence interval is smaller than in the cases above, but the real value can still lie anywhere between 8% and 15%. Meaning that if you opt for a laptop with 8GB memory instead 4, you should be prepared to pay 48% more.

Based on the regression coefficients, therefore, from the perspective of the price of the laptop

•  screen size is not important,
•  CPU size is not important,
•  an additional GB of memory can increase price by 11.6%,
•  hard drive size doesn’t matter,
•  having a GPU from a higher range can increase price by 32.4%,
•  having a touchscreen can increase price by 26.6%, and